In recent months Amazon has been keen to trumpet "record-breaking" sales of its electronic book reader, the Kindle. But the company's extreme secrecy means that nobody is sure quite how popular the device really is.

In November Amazon boasted that the gadget was its "most wished for, most gifted and number one best-selling product", and last week it said December was already the Kindle's best month yet. But it has refused to say exactly how many have been sold since the 2007 launch.

"Amazon has always been a secretive company. Companies like Amazon think that giving out information will help competitors," said Paul Biba, editor of Teleread, which tracks the electronic book industry.

Sandeep Aggarwal, an analyst with Collins Stewart in New York who has tracked the Kindle's performance, believes that across both models – the paperback-sized Kindle 2 and larger-screened DX – Amazon may be on target to have sold a little over 500,000 units by the end of the year. That would lag behind the pace set by Apple's iPod, which sold 376,000 in its first year on the market, in 2002, and almost 1m in its second year.

Even at that point, the iPod's dominance of the music market was not yet obvious. It was only in 2004, after Apple launched the iTunes download store in several countries, that sales began to increase dramatically. The company has now sold around 230m iPods worldwide.

There is no suggestion that Amazon's blockbuster descriptions of popularity are false, but a clearer picture of the truth may lie between the lines of its carefully chosen language. For example, the company says the Kindle is the "number one best-selling" product on Amazon.com. But because all worldwide sales of the gadget are routed through the company's US site, the chances are high that it will rank among these best-selling items.

Furthermore, Amazon is the only outlet through which the Kindle is available – unlike rival devices from the likes of Sony and others, which are sold through a variety of shops and websites.

An Amazon spokeswoman told the Guardian that Kindle sales were "not a figure Amazon discloses". Nor does it divulge data about the Kindle-compatible books it sells, even screening figures from the publishing industry's main monitoring group, Nielsen BookScan.

"Unfortunately, we do not currently capture ebook sales in our BookScan US system," said Nielsen's Dennis Halby. "Ebook data remains a major priority for us and we're currently working towards our goal of adding this data to our physical book sales data."

Without figures, it is hard for publishing companies and rival ebook makers to accurately gauge how popular is the market for their products. Last month the US book retailer Barnes & Noble launched its own Kindle competitor, the Nook.

"The Nook has sold out, much to the embarrassment of Barnes & Noble," said Teleread's Biba. "If Amazon had released its sales figures then maybe Barnes & Noble could have used these to plan better when ordering its first shipment of Nooks. Always keep the competition guessing."